论文标题
顺序广义似然比测试的非参数迭代式矩阵扩展
Nonparametric iterated-logarithm extensions of the sequential generalized likelihood ratio test
论文作者
论文摘要
我们为单变量分布的平均值开发了顺序概括性可能比率（GLR）测试的非参数扩展和相应的时间均匀置信序列。通过利用GLR统计量的几何解释，我们得出了一个简单的分析上限，它超过了任何预先指定的边界的概率；由于测试的无限范围和正在考虑的复合材料非参数零，这些因素与近似模拟相互棘手。使用时间均匀的边界交叉不平等，我们对非参数分布类别的单方面和开放式测试的预期样本量进行了统一的非扰动分析（包括亚高斯，高指数，尺度，亚伽马和指数族）。最后，我们提出了一种灵活且实用的方法，可以构建时间均匀的置信序列，这些置信序列易于调谐，可以在任何目标时间间隔上均匀地接近Chernoff绑定。
We develop a nonparametric extension of the sequential generalized likelihood ratio (GLR) test and corresponding time-uniform confidence sequences for the mean of a univariate distribution. By utilizing a geometric interpretation of the GLR statistic, we derive a simple analytic upper bound on the probability that it exceeds any prespecified boundary; these are intractable to approximate via simulations due to infinite horizon of the tests and the composite nonparametric nulls under consideration. Using time-uniform boundary-crossing inequalities, we carry out a unified nonasymptotic analysis of expected sample sizes of one-sided and open-ended tests over nonparametric classes of distributions (including sub-Gaussian, sub-exponential, sub-gamma, and exponential families). Finally, we present a flexible and practical method to construct time-uniform confidence sequences that are easily tunable to be uniformly close to the pointwise Chernoff bound over any target time interval.
